Question

A merchant blends tea that sells for $4.75 a pound with tea that sells for $2.50 a pound to produce 110 lb of a mixture that sells for $3.85 a pound. How many pounds of each type of tea does the merchant use in the blend?

Answer 1

The merchant uses 60 pounds of tea that sells for $4.75 per pound and 50 pounds of tea that sells for $2.50 per pound in the blend.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.

Let's say the merchant uses x pounds of tea that sells for $4.75 per pound, and y pounds of tea that sells for $2.50 per pound.

We can use the information given to set up the following equations:

• x + y = 110 (equation 1, representing the total weight of the mixture)
• (4.75x + 2.50y) / 110 = 3.85 (equation 2, representing the average price per pound of the mixture)

We can solve this system of equations to find the values of x and y.

From equation 1, we can isolate x to get x = 110 - y.

Substituting this into equation 2, we get (4.75(110 - y) + 2.50y) / 110 = 3.85.

Simplifying and solving for y, we find y = 50.

Substituting this value into x = 110 - y, we find x = 60.

Therefore, the merchant uses 60 pounds of tea that sells for $4.75 per pound and 50 pounds of tea that sells for $2.50 per pound in the blend.